对数能力测试卷 8

正确选项：C

解决方案

已知,

log√2(32)

= log2^1/2(32)

= 1/(1/2) * log2(32) …. [loga^b(c) = 1/b * loga(c)]

= 2 * log2(2^5)

= 2 * 5 * log2(2)

= 2 * 5 * 1 …. [log2(2) = 1]

= 10

正确选项：C

解决方案

已知,

a^x = b^y

两边取对数，

⇒ log(a^x) = log(b^y)

⇒ x * log(a) = y * log(b) …. [log(a^b) = b log(a)]

⇒ log a/log b = y/x

因此，C 选项是正确的。

正确选项：B

解决方案

x, y, z 是直角三角形的边，其中 'z' 是斜边。

⇒ x^2 + y^2 = z^2

⇒ x^2 - z^2 = y^2 …. (1)

已知,

(1/logx + zy) + (1/logx - zy)

= logy(x + z) + logy(x - z) …. [logx(y) = 1/logy(a)]

= logy((x + z) * (x - z)) …. [log(m) + log(n) = log(m * n)]

= logy(x^2 - z^2)

= logy(y^2) …. 根据 (1)

= 2 logy(y)

= 2 …. [logaa = 1]